Suppose the short-run production function for a particular product - 39862

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Suppose the short-run production function for a particular product is represented by:

Q = 60,000L2 – 1,000L3

a. Find the marginal product and show mathematically that labor is subject to diminishing returns.
b. Beyond what labor usage, the marginal product becomes negativec.
c. Show mathematically that when the average product is at maximum, marginal product is equal to it?

Solution Description

(a) MP(L) = dQ/dL = 120000L - 3000L^2

The MP(L) curve is a parabola which opens downwards. This means MP(L) 

diminishes after reaching a maximum value.